Question

1
20.
Example 3: Find the mean proportion of the numbers 3, 12.
Solution: Let the mean proportion be x.
So,
3:x:: x: 12
3
х
I/
X
12
x2
Or
3 x 12
36
Therefore
6.
Therefore the mean proportion of numbers 3, 12 is 6.
X =
5
15
Exercise 9.2
1. Which of the following ratios are in proportion?
a) 4, 8, 16, 32
b) 9, 18, 20, 52
bortion
co​

Answer 1

Answer:

Therefore, 2.5, 3.5 and x are in continuous proportion.

 \(\frac{2.5}{3.5}\) = \(\frac{3.5}{x}\)

⟹ 2.5x = 3.5 × 3.5

⟹ x = \(\frac{3.5 × 3.5}{2.5}\)

⟹ x = 4.9 g

2. Find the mean proportional of 3 and 27.

Solution:

The mean proportional of 3 and 27 = +\(\sqrt{3 × 27}\) = +\(\sqrt{81}\) = 9.

 

3. Find the mean between 6 and 0.54.

Solution:

The mean proportional of 6 and 0.54 = +\(\sqrt{6 × 0.54}\) = +\(\sqrt{3.24}\) = 1.8

 

4. If two extreme terms of three continued proportional numbers be pqr, \(\frac{pr}{q}\); what is the mean proportional?

Solution:

Let the middle term be x

Therefore, \(\frac{pqr}{x}\) = \(\frac{x}{\frac{pr}{q}}\)

⟹ x\(^{2}\) = pqr × \(\frac{pr}{q}\) = p\(^{2}\)r\(^{2}\)

⟹ x = \(\sqrt{p^{2}r^{2}}\) = pr

Therefore, the mean proportional is pr.

 

5. Find the third proportional of 36 and 12.

Solution:

If x is the third proportional then 36, 12 and x are continued proportion.

Therefore, \(\frac{36}{12}\) = \(\frac{12}{x}\)

⟹ 36x = 12 × 12

⟹ 36x = 144

⟹ x = \(\frac{144}{36}\)

⟹ x = 4.